Is this sequence arithmetic or geometric?
List at least 5 terms of the sequence
Write a recursive definition for the sequence

Step-by-step explanation:

what is missing is the definition that QS is the height and therefore standing at a right angle (90°) at PR.

then this can be solved.

we use Pythagoras

c² = a² + b²

c being the Hypotenuse (the side opposite of the 90° angle), a and b are the legs.

let's start with the triangle PQS.

21² = 15² + QS²

441 = 225 + QS²

QS² = 216

QS = sqrt(216) = sqrt(36×6) = 6×sqrt(6) = 14.69693846...

now for triangle QSR

(5x - 16)² = (3x - 4)² + QS²

25x² - 160x + 256 = 9x² - 24x + 16 + 216

16x² - 136x + 24 = 0

2x² - 17x + 3 = 0

the solution to a quadratic equation

ax² + bx + c = 0

is

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

x = (17 ± sqrt(17² - 4×2×3))/(2×2) =

= (17 ± sqrt(289 - 24))/4 = (17 ± sqrt(265))/4

x1 = (17 + 16.2788206...)/4 = 8.319705149...

x2 = (17 - 16.2788206...)/4 = 0.180294851...

but using x2 in side lengths 3x - 4 or 5x - 16 gives us negative side lengths. that does not make any sense for actual side lengths.

so, x1 is our solution :

x = 8.319705149...

The constant of proportionality is equal to 6.

In Mathematics, a proportional relationship is a type of relationship that generates equivalent ratios and it can be modeled or represented by the following mathematical expression:

y = kx

Where:

Next, we would determine the constant of proportionality (k) for the relationship between correct answers and points on this graph as follows:

Constant of proportionality, k = y/x

Constant of proportionality, k = 30/5 = 72/12 = 108/18 = 120/20

Constant of proportionality, k = 6

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Answer:

6

Step-by-step explanation:

120/20 = 6

108/18 = 6

72/12 = 6

30/5 = 6

See the pattern? :)

The given relationship is such that 1 / z⁴ = z ⁻⁴.

When given 1 / z⁴, this can be rewritten in such a way that it becomes z ⁻⁴.

This is because when a denominator is raised to a exponent , it can be transformed to a numerator if the sign on the power is changed to the negative.

This means that when the fraction was 1 / z⁴, it can become the value of z ⁻⁴ because the negative in front of the 4 shows that it is a fraction.

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The given initial value problem y(0)=8, solution is [tex]y=\sqrt{64e^x-3x}[/tex]

Any equation with at least one ordinary or partial derivative of an unknown function is referred to as a differential equation. Assuming that a function's rate of change with regard to x is inversely proportional to y, we may write it down as dy/dx = k/y. An equation involving the derivative (derivatives) of the dependent variable with respect to the independent variable is referred to as a differential equation in calculus (variables). The differential equation assists us in presenting a relationship between the changing quantity with respect to the change in another variable. The derivative represents nothing more than a rate of change. If y is a dependent variable, f is an unknown function, and x is an independent variable, then y=f(x) is a function.

The given differential equation is,

[tex]2yy'+3=y^2+3x\\\\2y\frac{dy}{dx}=y^2+3x-3\\\\(3-y^2-3x)dx+2ydy=0\\\\compare, Mdx+Ndy=0\\\\M=3-y^2-3x\\\\N=2y[/tex]

The given equation is not exact but if we multiplied by [tex]e^{-x}[/tex]

[tex]The D.E.\\(3-y^2-3x)e^{-x}dx+2ye^{-x}dy=0\\\\then M_y=-2ye^{-x}=N_x\\The G.S,=y^2e^{-x}+3xe^{-x}=c\\\\y(0)=8\\c=64\\hence,\\y=\sqrt{64e^x-3x}[/tex]

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Answer:

The slope of a line is represented by the coefficient of the x-term in the equation, which is also known as the "rise over run" or change in y over change in x.

In this equation y = 29/8x - 2/3

The coefficient of the x-term is 29/8, so the slope of the line is 29/8.

By Simplify  expression  -9y-10y -2z  this we get - 19y - 2z.

Examples :

-9y-10y -2z

Simplify

-9y - 10y - 2z : -19y - 2z

-9y - 10y - 2z

= - 19y - 2z.

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Average rate of change for the first 10 minutes after the soup was placed in the bowl is 200 .

220 +180/2 = 200

average rate of change for the first 10 minutes after the soup was placed in the bowl 200.

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Trapezoid PQRS having vertices P(0, 0), Q(0, 4), R(6, 4), and S(12, 0),

has the length of the midsegment as 11.07 units.

What is a trapezoid?

A polygon with only one set of parallel sides is called a trapezoid. The parallel bases of a trapezoid are another name for these parallel sides. Trapezoids have two additional sides that are not parallel and are referred to as their legs.

The length of the mid segment of trapezoid is half the sum of the lengths of the two parallel sides, PQ and RS.

The points for vertices are given as - P(0, 0), Q(0, 4), R(6, 4), and S(12, 0).

Length of sides PQ and RS is given as -

The line segment PQ = √(x2 - x1)² + (y2 - y1)²

PQ = √(0 - 0)² + (4 - 0)²

PQ = √0² + (4)²

PQ = √0 + 16

PQ = √16

PQ = 4 units

The line segment RS = √(x2 - x1)² + (y2 - y1)²

RS = √(12 - 6)² + (0 - 4)²

RS = √(6)² + (-4)²

RS = √36 + 16

RS = √50

RS = 5√2 units

To find the mid segment add the length of PQ and RS.

So, the equation will be -

Midsegment = PQ + RS

Midsegment = 4 + 5√2

Midsegment = 11.07 units

Therefore, the length of midsegment is 11.07 units.

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Answer: 9

Step-by-step explanation: (6+12) / 2 = 9

Answer:

slope = 1/2

Step-by-step explanation:

rise = 3

run = 6

rise/run

3/6 = 1/2

Answer:

The slope is 1/2

Step-by-step explanation:
The slope is rise over run, from point 1 to point 2 the line rises 3.
The run from point 1 to point 2 is 6.

That means that rise over run is 3/6
Simplify this so that it is in the simplest form to get 1/2.

The image shows the rise and the run.

I hope this helps you out :D

Answer: Net (of a shape)

Step-by-step explanation:

Answer:

Step-by-step explanation:

no need for step by step its called a net

Answer:

= 7n − 3 emde n = 1, 2, 3, ...

A symmetric matrix is a square matrix that is equal to transpose of itself. If A is a symmetric matrix, then it satisfies the condition: A = AT. (AT is the inverse of A )

A square matrix with real numbers or elements is said to be an orthogonal matrix if its transpose is equal to its inverse matrix. Or we can say when the product of a square matrix and its transpose gives an identity matrix, then the square matrix is known as an orthogonal matrix.

Suppose  λ and  μ are 2 distinct values of matrix  A.

For the matrix to be Symmetric,

                 ( Ax,y)=(x,Ay)

 condition needs to be satisfied.

Here, ( x,y) is dot product between vectors  x and  y

                 λ (u,v) = (λu,v)

 where  u,v are eigen vectors for eigen values  λ and  μ

             λ(u,v) = (Au,v)

             λ(u,v) = (u,Av)

             λ(u,v) = μ(u,v)

             λ(u,v) = μ(u,v)

but  λ≠μ

                             ∴ (u,v) = 0.

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The complete question is :

If a matrix is symmetric then show that any two eigenvectors of that matrix corresponding to different eigenvalues are orthogonal. Assume square matrix.

We can see here that the people of ages 18-29 that have tried vaping or e-cigarettes is: 25,803,450.

Population refers to the number of individuals of a particular species living in a particular area or region. In the context of human populations, it refers to the number of people living in a particular geographic area or country.

To find out the number of people ages 18-29 who said they have tried vaping or e-cigarettes, you can use the following calculation:

30,357,000 (the number of people ages 18-29) x 0.85 (the percentage of people who have tried vaping or e-cigarettes) = 25,803,450.

So, approximately 25,743,950 people ages 18-29 said that they have tried vaping or e-cigarettes.

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The joint probability mass function given by PX, Y(a, b) = {1/4a, for 1≤ b≤a≤4, otherwise is indeed a joint probability mass function because the sum of all the joint probabilities is equal to 1.

To find the marginal probability mass function of X, we need to sum the joint probabilities over all possible values of Y:

PX(a) = ∑ PX, Y(a,b) = ∑ (1/4a) = 1/4

To find the marginal probability mass function of Y, we need to sum the joint probabilities over all possible values of X:

PY(b) = ∑ PX, Y(a,b) = ∑ (1/4a) = 1/4

To find P(X = Y + 1), we need to find the joint probability of X = a and Y = a-1, where a = 2,3.

P(X = Y + 1) = PX, Y(2,1) + PX, Y(3,2) = (1/42) + (1/43) = 1/4 + 3/12 = 5/12

So the probability that X is one more than Y is 5/12.

It's important to note that the given joint probability mass function is valid as it satisfies the non-negativity and the condition of summing to 1.

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When two pairs of corresponding angles and the included pair of sides are likewise congruent, a triangle is said to be congruent.

When two triangles can be superimposed, have identical side lengths, and equal angles, they are said to be congruent.

Triangles with the same angle measurements and side lengths are said to be congruent. SSS (Side-Side-Side) SAS are the triangle congruence criteria (Side-Angle-Side). When they have, triangles are congruent. There are precisely the same three sides and three angles.

Triangles are said to be congruent if two pairs of corresponding angles and the included pair of sides are also congruent. The triangles are congruent if a pair of sides that are not included and two pairs of comparable angles are congruent.

When the coordinates of XYZ are converted to produce its congruent image, X'Y'Z.

The triangle XYZ's translated picture is X'Y'Z'.

The triangle XYZ's reflected image becomes X'Y'Z'.

The triangle XYZ does not turn into its rotated counterpart, X'Y'Z'.

Therefore, Option I and II are true statements. so D is the correct answer.

The complete question is:

XYZ is transformed on a coordinate plane to obtain its congruent image X'Y'Z. Which of the following statements could be true?

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The shingles are in the 6th row is 110 using arithmetic process.

A subject of mathematics known as arithmetic operations deals with the study and use of numbers in all other branches of mathematics. Basic operations including addition, subtraction, multiplication, and division are included.

The study of numbers and the operations on those numbers, which are relevant to all other branches of mathematics, is the focus of a branch of mathematics known as arithmetic operations. It includes addition, subtraction, multiplication, and division as its fundamental operations.

Given that A = 75 and d = 7, n = 6

A₆ = A + (n-1)d

A₆ = 75 + (6-1)7

A₆ = 75 + 5 * 7

A₆ = 75 + 35

A₆ = 110

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Answer:

33

Step-by-step explanation:

it starts with 75 and decreases by 7 for each row. on the 6th row youll be at 33!

STARTS AT 75

row one: 68

row two: 61

row three:54

row four: 47

row five: 40

row six: 33

Answer:

there's ur answer ...........

Answer:

A solution of an equation is any value of the variable that satisfies the equality, that is, it makes the Left Hand Side (LHS) and the Right Hand Side (RHS) of the equation the same value. To solve an equation is to find the solution(s) for that equation.

Step-by-step explanation:

The terms mean median, mode, and range describe properties of statistical distributions.

The statistical distributions' characteristics are described by the terms mean, median, mode, and range. The set of all potential values for terms that indicate predetermined events is known as a distribution in statistics. A term's value stated as a variable is referred to as a random variable.

The two main categories of statistical distributions are as follows. There are discrete random variables in the first category. This indicates that each phrase has a distinct, precise numerical value. A continuous random variable is present in the distribution of the second major kind. An unlimited number of possible values can be represented by a continuous random variable. A term is said to have a probability density function when any value can be assigned to it within an uninterrupted interval or span.

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Answer:

B

Step-by-step explanation:

Trust

Simply multiply each value of the discrete random variable by the probability associated with that value to obtain the expected value, E(X), or mean. E(X)=xP is the formula's notation (x).

f(x) = 4x³,0 < x < 1

Domain of f(x) = 4x³,0 < x < 1 : Solution : 0 < x < 1

Interval notation : (0,1)

Range of 4x³ ,0 < x < 1;

Solution : 0 < f(x) < 4

Interval Notation : (0,4)

Axis interception points of 4x³,0 <x <1.

Asymptotes of 4x³. 0 < x < 1;

Extreme Points of 4x³ . 0<x < 1:

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The probabilities of adults who drinks only coffee , both/ coffee ,soda and doesn't drink any are 5% , 65% and 35%.

Let A be the event that an adult consumes coffee.

Let B be the event that an adult consumes carbonated soda.

Given probabilities of the events.

P (A) = 0.4

P (B) = 0.6

P(A∩B) = 0.35

(a). P(A)  - P(A∩B) = 0.4 - 0.35

                             = 0.05 OR 5 %

(b). P(AUB) = P (A) + P (B) - P(A∩B)

                   = 0.4 + 0.6 - 0.35

                   = 0.65 OR 65%

(c). The given case represents compliment of the event when the adult consumes at least one of the drink. According to probability axiom, the probability is given by:

P ((AUB)') = 1 - P (AUB) = 1-0.65 = 0.35

Therefore,

P ((AUB)') = 0.35 or 35 %.

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Answer:

x = 1, y = - 5

Step-by-step explanation:

2x + 2y = - 8 → (1)

- 13x + 7y = - 48 → (2)

multiplying (1) by 7 and (2) by - 2 and adding will eliminate y

14x + 14y = - 56 → (3)

26x - 14y = 96 → (4)

add (3) and (4) term by term to eliminate y

40x + 0 = 40

40x = 40 ( divide both sides by 40 )

x = 1

substitute x = 1 into either of the 2 equations and solve for y

substituting into (1)

2(1) + 2y = - 8

2 + 2y = - 8 ( subtract 2 from both sides )

2y = - 10 ( divide both sides by 2 )

y = - 5

then solution is x = 1, y = - 5

The probability of picking a second black marble is 4/13

Probability is the likelihood that an event will occur and is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.

Probability helps us know the chance an event has to occur. The closer it gets to zero(0) the less chance it has to occur. The closer it gets to one(1) the more chance it has to occur.

Therefore, The probability of picking a second black marble is 4/13

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The option are :

4/13

85/182

25/637

45/182

The correct answer is d.  The standard form of the equation of f(x) is −x2 + 6x + 16.

A downward opening parabola is a curve in the shape of a parabola that opens downward and is symmetrical about the x-axis. The equation of a downward opening parabola is y = ax^2 + bx + c, where a is a negative number, and b and c are constants.

The focus of a downward opening parabola is the point on the parabola where the curvature is greatest and is located at the vertex of the parabola.

The directrix of a downward opening parabola is a line parallel to the x-axis and the distance from the focus to the directrix is equal to the length of the latus rectum of the parabola. The equation of the directrix is y = -a(x - h)^2 + k, where h and k are constants.

Downward opening parabolas can be used to graphically represent any type of data that follows a parabolic shape. This includes physical phenomena such as the path of a projectile or the vibration of a string.

Downward opening parabolas can also be used to model economic or financial data, such as the demand for a product or the price of a commodity. They may also be used to describe relationships between two variables in a mathematical equation.

The standard form of a parabola equation is f(x) = ax2 + bx + c, where a, b, and c are real numbers. In this case, the vertex of the parabola is at (3, 25), so the equation is in the form f(x) = a(x - 3)2 + 25. Putting in the other points on the graph to solve for a, b, and c yields the equation f(x) = -x2 + 6x + 16.

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The temperature of the cup if it is left alone for 20 minutes, can be found to be 97 degrees Fahrenheit

To find the tempertature of the cup, the formula would be:

= Beginning temperature x ( 1 - rate of decrease per minute  ) ^ number of minutes

Beginning temperature = 185 degrees fahrenheit

rate of decrease per minute = 3.2% each minute

number of minutes  = 20 minutes

The temperature is:

= 185 x ( 1 - 3 .2 %) ²⁰

= 97 degrees Fahrenheit

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